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You should try achieving what you want and see how it goes. Doing that will answer most of your questions.

You never use an atlas in the Spine editor. Atlases are for runtime.

Images are found by name in the editor:
https://esotericsoftware.com/spine-images#Image-file-lookup

They are also found by name in an atlas at runtime. Multiple skeletons can use the same atlas, as long as it contains the regions (by name) that the skeleton needs.

    Nate I now package the maps that need to be used in common into several shared textures, and then use them in different spine projects, but there is a question, can spine set different material slots? I want the same Spine Mecanim GameObject to have different material slots. I need to give a single spine character different materials.

    Nate thank you for your reply and we can close the quastion or issue, I get the correctly mothed and I know I don't need the public texture 😅